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Simplifying (2x + 8)(3x + -6) = -10 Reorder the terms: (8 + 2x)(3x + -6) = -10 Reorder the terms: (8 + 2x)(-6 + 3x) = -10 Multiply (8 + 2x) * (-6 + 3x) (8(-6 + 3x) + 2x * (-6 + 3x)) = -10 ((-6 * 8 + 3x * 8) + 2x * (-6 + 3x)) = -10 ((-48 + 24x) + 2x * (-6 + 3x)) = -10 (-48 + 24x + (-6 * 2x + 3x * 2x)) = -10 (-48 + 24x + (-12x + 6x2)) = -10 Combine like terms: 24x + -12x = 12x (-48 + 12x + 6x2) = -10 Solving -48 + 12x + 6x2 = -10 Solving for variable 'x'. Reorder the terms: -48 + 10 + 12x + 6x2 = -10 + 10 Combine like terms: -48 + 10 = -38 -38 + 12x + 6x2 = -10 + 10 Combine like terms: -10 + 10 = 0 -38 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying -19 + 6x + 3x2 = 0 Solving -19 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + 2x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + 2x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + 6.333333333 2x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 2x + x2 = 6.333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 6.333333333 + 1 Reorder the terms: 1 + 2x + x2 = 6.333333333 + 1 Combine like terms: 6.333333333 + 1 = 7.333333333 1 + 2x + x2 = 7.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 7.333333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (x + 1) equal to 2.708012801 and -2.708012801.Subproblem 1
x + 1 = 2.708012801 Simplifying x + 1 = 2.708012801 Reorder the terms: 1 + x = 2.708012801 Solving 1 + x = 2.708012801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.708012801 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.708012801 + -1 x = 2.708012801 + -1 Combine like terms: 2.708012801 + -1 = 1.708012801 x = 1.708012801 Simplifying x = 1.708012801Subproblem 2
x + 1 = -2.708012801 Simplifying x + 1 = -2.708012801 Reorder the terms: 1 + x = -2.708012801 Solving 1 + x = -2.708012801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.708012801 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.708012801 + -1 x = -2.708012801 + -1 Combine like terms: -2.708012801 + -1 = -3.708012801 x = -3.708012801 Simplifying x = -3.708012801Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.708012801, -3.708012801}Solution
x = {1.708012801, -3.708012801}
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